PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Becky Halpenny.

Title:"Long-time Behavior of Stochastic Models"
Seminar:Ph.D. Oral Comprehensive Examination
Speaker:Chao Tian, Adviser: Qiang Du, Penn State
Abstract:
In this talk, I will present two examples to illustrate the rich long time dynamics of stochastic models. The first example is related to fluid-structure interaction (FSI) which appears in many scientific and engineering problems. The stochastic implicit-interface method (SIIM) is designed to account for the microscopic fluctuation in phase-field or level-set models of FSI. Formulated as a system of non-linear stochastic partial differential equations with a degenerate additive noise term, the SIIM is formally derived using the fluctuation-dissipation theorem. It is interesting to study its long time asymptotic behavior. The second example is a bi-stable mean-field model whose mathematical analysis, including the study of mean-field limits, existence of multiple equilibria, and fluctuation theory was initiated by D.A. Dawson et al. Using the large-deviations theory G. Papanicolaou et al. recently studied the dynamical phase-transitions in such systems due to stochastic fluctuation. We consider various generalizations of such mean-field models and study the phase transitions between different equilibria in various settings.

Room Reservation Information

Room Number:104 Osmond
Date:04 / 29 / 2013
Time:01:00pm - 03:00pm